Let u and v be nonzero vectors in an inner product space V. Prove that $u-projv(u)$ is or orthogonal to v.

Question

I do know that the question is asking to prove $\langle u-\operatorname{proj}_v(u),v \rangle =0$. But I don't know how to prove it.

By the way, an inner product is not a dot product. I know how to prove it, if $\langle u,v \rangle=u\bullet v.$